Class Date |
Section(s) Covered |
Topics |
Jan. 10 |
Chapter 2 |
introduction to course, definition and basic examples of groups |
Jan. 12 |
Chapter 2 and Chapter 0 |
basic properties of groups |
Jan. 14 |
Chapter 0 |
basic properties of integers |
Jan. 19 |
Chapter 0 |
basic properties of integers, equivalence relations |
Jan. 21 |
Chapter 0 |
equivalence relations |
Jan. 24 |
Chapter 0 |
equivalence relations, modular arithmetic |
Jan. 28 |
Chapter 0 |
modular arithmetic |
Jan. 31 |
Chapter 0 and Chapter 2 |
Z/nZ |
Feb. 2 |
Chapter 0 and Chapter 2 |
U(n), induction, other examples of groups |
Feb. 4 |
Chapter 3 |
order of a group, subgroups |
Feb. 7 |
Chapter 1 |
dihedral groups |
Feb. 9 |
Chapter 3 |
center and centralizers |
Feb. 11 |
Chapter 4 |
cyclic groups |
Feb. 14 |
Chapter 4 |
cyclic groups |
Feb. 16 |
Chapter 4 |
cyclic groups |
Feb. 18 |
Chapter 5 |
permutation groups |
Feb. 21 |
Exam 1 |
Chapter 0 through Chapter 4 |
Feb. 23 |
Chapter 6 |
isomorphisms |
Mar. 7 |
Chapter 5 |
permutation groups |
Mar. 9 |
Chapter 8 |
direct products |
Mar. 11 |
Chapter 6 |
isomorphisms |
Mar. 14 |
Chapter 6 |
isomorphisms |
Mar. 16 |
Chapter 6 |
isomorphisms |
Mar. 18 |
Chapter 6 |
automorphisms |
Mar. 21 |
Chapter 10 |
homomorphisms |
Mar. 23 |
Chapter 10 and Chapter 7 |
Cayley's Theorem and cosets |
Mar. 25 |
Chapter 7 |
cosets |
Mar. 28 |
Chapter 7 |
Lagrange's Theorem |
Mar. 30 |
Chapter 7 |
applications of Lagrange's Theorem |
Apr. 1 |
Chapter 9 |
factor groups of abelian groups |
Apr. 4 |
Exam 2 |
Chapter 5 through Chapter 8, Chapter 10 |
Apr. 6 |
Chapter 9 |
normal subgroups |
Apr. 8 |
Chapter 9 |
factor groups |
Apr. 11 |
Chapter 10 |
isomorphism theorems |
Apr. 13 |
Chapter 9 and Chapter 12 |
internal direct products and introduction to rings |
Apr. 15 |
Chapter 12 and Chapter 13 |
properties of rings and integral domains |
Apr. 18 |
Chapter 14 |
ideals |
Apr. 20 |
Chapter 16 |
polynomial rings |
Apr. 26 |
Chapter 16 and Chapter 17 |
polynomial rings and factoring |
Apr. 27 |
- |
introduction to my research |
May. 4 |
Final Exam |
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